Difference basically is case size of the 3006(long action rifle) is larger allowing more powder to fling the same sized .308 diameter bullets faster, flatter, harder and really further in hunting terms.

I agree for a good deer caliber, very easy on shoulder, fairly versatile & cheap to plink stuff with the .308 win would be a good choice. The 3006 or 270 win would also fit your requirement and ammo is about the same in terms of cost/availability. The 3006 has more grain choice but really for the bulk of user it is rarely harnessed. I personally like the 270 better for deer type duty. When something slightly larger is required/desired I like the .284's in a 280 rem or in my case a 7mm rem mag.